A lot can happen in 13 years. In the gap between Zdenek Zeman's 1999 dismissal by Roma and his return to that club this summer, DVDs have replaced VHS tapes, Blu-Ray discs have replaced DVDs and the internet has rendered all three mediums obsolete. Palermo have gone through more than 25 managerial changes and Antonio Cassano through more than 600 sexual partners – still having time after that to settle down, get married and have a child.

Watching Zeman's team take on Internazionale at San Siro on Sunday night, though, you may have come to the conclusion that some things had not changed at all. In only his second competitive game back in charge, the manager had his team pressing, chasing and attacking their opponents just like they had in the best moments of his previous tenure. And there, pulling the strings, was the same player Zeman had always rated most highly of all.

"Totti, Totti and Totti," was Zeman's famous reply when asked to name the three best players in the country some time after his departure from Roma. Reminded of those words during an interview in 2010, Zeman remained convinced of the player's merits. "Physically he is not what he was before," he said. "But with the ball at his feet he is still the best."

Another two years on, Totti is approaching his 36th birthday and believed by many to have endured a significant erosion of his powers in the interim. "Il caso Totti" – the Totti issue – has been a regular discussion point ever since his signing of a new five-year playing contract in November 2009, reporters and fans debating how best Roma could manage his enduring prominence within the team but diminishing ability to influence a match.

By the end of Sunday night, such conversations had been made to feel rather silly. Totti had provided two assists in a 3-1 victory – Roma's first over Inter at San Siro since 2007 – but even that did not begin to tell the story of an evening in which he had been simply sublime: a masterclass of fabulous feints, crafty flicks and slick passing that left Inter chasing shadows.

It was Totti who had first unpicked the Inter defence after 15 minutes, whisking over a cross from the left to be glanced into the far corner of Luca Castellazzi's net by Alessandro Florenzi, the latter making his first ever start for the senior team. After Cassano had levelled the scores with a fortuitous deflected strike before half-time, it was Totti again who released Pablo Daniel Osvaldo with a brilliant 30-yard through ball that allowed the latter to restore their lead.

"For that assist he will have to buy me dinner," Totti said of his team-mate – who had later been sent off for a second booking. "Before the second half began we made an agreement: either he or I was going to have to score a goal."

Such conversations reflect the mindset of Zeman's team, a core belief that the best route to victory is always to keep on attacking. Roma had suffered injuries to two key players – Daniele De Rossi and Federico Balzaretti – during the game yet even once they had restored their lead continued to pour forward, earning their reward when the substitute Marquinho crashed their third home from a tight angle.

The starting lineup, indeed, had told you everything you would need to know about the manager's approach – Totti and Osvaldo starting alongside another would-be centre-forward, Mattia Destro, up front. What was nominally 4-3-3 became something rather more nuanced as Totti drifted deep and inside from his starting position on the left.

Indeed, from a tactical standpoint this was not classic Zeman – his team lacking the consistent width he would usually seek – but the fundamental premise was the same. Right from kick-off, his team sought to press Inter high up the pitch, the youthful energy of Florenzi and Panagiotis Tachtsidis helping to pin their hosts in. In possession, Roma were quick and direct – showing far less of the "pointless" sideways passing that so infuriated Zeman during their draw with Catania last week.

Totti was quick to play down the significance of the result, calling for a level-headed assessment of his team's start. "Let's wait before saying that something new is being born because in Rome we are quick to celebrate and also to get down on ourselves, and these ups and downs don't do us any good," he said. "We need to keep our feet on the ground and try to play like this in every match. It won't be easy, but we'll try."

Zeman, though, was in no mood to temper anybody's enthusiasm. "No, it makes me happy," he replied when asked whether he feared the sense of euphoria generated by such a win. "I always want more people to come out and support the team. We play football for them." In response to a further question about whether his team had earned the right to dream big this year, he said: "We should not dream. We should work hard so we can let others dream."

It is this belief in football as a public good which is perhaps what renders Zeman and his teams so exciting. His outspoken commitment to fair play has made him popular with supporters of many teams he has never coached, and on Sunday Inter supporters in the Curva Nord revealed a banner reading: "Honour to Zeman: an icon of clean football." Zeman said: "It makes me very happy. But I hope they could write that banner without my name too."

Inter's own manager, Andrea Stramaccioni, counts himself among Zeman's admirers – having himself grown up in Rome as a fan of the Giallorossi, eventually building his reputation as a coach in the team's youth setup. His time there had coincided with Florenzi's rise through the ranks. "He's a good player and that was a nice goal. I want a cut," observed Stramaccioni with a wry smile.

Inter had been outplayed by their visitors but Stramaccioni insisted that the issue was a psychological one – suggesting they had allowed their heads to drop after Roma's second goal. It had not been an awful performance, by any means, and, though there was much that could have been improved, the debut of the new signing Alvaro Pereira on the left of midfield was encouraging. It did not go unnoticed that Roma's second arrived immediately after he had been substituted.

The one great concern for the Nerazzurri is their home form. Early days it may be, but thus far between Serie A and the Europa League, Inter have won all three of their away games this season – scoring eight goals and conceding none. At home they have drawn one and lost two, conceding seven goals and scoring just three.

They are a team still finding their identity under Stramaccioni, something that is perhaps to be expected with such a new coach in charge of a team that underwent significant turnover in its playing staff over the summer. Unlike with Zeman and Totti at Roma, there are no relationships here which have been over a decade in the making.

Talking points

• One theory for Inter's struggles at home relates to the new pitch laid at San Siro over the summer – a partially synthetic surface along the lines of those seen at Novara and Cesena last season. Milan, too, have lost their only home game so far this season (both if you count the pre-season Trofeo Berlusconi) – though it is not much of an excuse. After all, their visitors will of course be just as unfamiliar with the surface.

• It should also be pointed out that the new pitch at San Siro is – at this very early stage – holding up very well, which is more than can be said for several others. Such was the state of the field at Napoli's Stadio San Paolo that Sky Sport likened their match against Fiorentina to "beach football". "We need to do something fast, the pitch is dangerous," said Napoli's coach, Walter Mazzarri, stating the hope that action could be taken in time for their game against Parma on 16 September. It did not hurt his team in the short-term, at least, Napoli beating Fiorentina 2-1.

• Roberto Di Matteo was on hand to watch Juventus demolish Udinese 4-1 on Sunday afternoon, with Sebastian Giovinco scoring twice to help alleviate concerns about the failure to sign the promised "top player" up front. Defeat compounded a miserable start to the season for the Friuliani following their Champions League play-off defeat in midweek, and the team's owner, Giampaolo Pozzo, placed the blame squarely with referee Paolo Valeri, who sent off the goalkeeper Zeljko Brkic after awarding Juventus a penalty in the eighth minute. "Every time he comes to Udine he ruins the match," Pozzo said – citing a red card shown to Gokhan Inler two years previously as supporting evidence.

• Atalanta, meanwhile, had two penalties awarded against them in the space of eight minutes during their game at Cagliari – only for Andrea Consigli to save both. If Cagliari will lament the result – a 1-1 draw – then their players can at least claim victory in their campaign against playing games 500 miles away in Trieste. The team had not been able to acquire full safety clearance at their temporary home at the Stadio Is Arena, but players threatened to strike when informed that they would have to return to Trieste – where they played a number of "home" games at the end of last season. Instead this week's match was indeed played at the Stadio Is Arena – but behind closed doors.

• Another week, another win for newly promoted Sampdoria – who beat Siena 2-1 at the Stadio Luigi Ferraris. They would be joint top of the table along with Juventus, Napoli and Lazio (the last of these 3-0 winners at home to Palermo) were it not for the one-point deduction they received as a consequence of this summer's match-fixing investigations.

• Behind them in the standings, but feeling considerably brighter about the immediate future are Milan – after Giampaolo Pazzini got off the mark with a hat-trick in their 3-1 win at Bologna. "This is a message to all those who believed in me," Pazzini said, and his message will doubtless have been received loud and clear by former employers Inter following their defeat to Roma a day later.